Chapter 8: Aggregate Expenditure and Equilibrium …publish.illinois.edu/zzhangecon/files/2014/09/Chapter8_slides.pdfAggregate Expenditure Model Practice Essay Question 4 Chapter 8:

Aggregate Expenditure ModelPractice Essay Question 4

Chapter 8: Aggregate Expenditure and EquilibriumOutput

Week 4

Presenter:Zheng Zhang

February 15, 2013

Zheng Zhang Chapter 8: Aggregate Expenditure and Equilibrium Output


Table of Contents

1 Aggregate Expenditure Model

2 Practice Essay Question 4



John Maynard Keynes

Figure 1: John Maynard Keynes (1883-1946)



Basic Assumptions

Basic Assumptions in Aggregate Expenditure (Keynesian Cross)Model

(a) Vision: Short run

(b) Prices: Wages, Interests,Rents,Prices are STICKTY or fixed

(c) Agents: Household and Business Sectors, No GovernmentSector.

(d) Scope: Closed Economy, No Trade(thus no export and import)

(e) Variables: Planned Investment (I) is exogenous but C, Y areendogenous .



Keynesian Cross in Circular Flow Diagram

Figure 2: The Circular Flow Diagram with Households and Firms



Learning Objectives

Understanding Consumption(Saving) Function both in Algebraand Geometry.(2012Mid1 M28 ; M29; M30 ; M31; M32; M33; )

Understanding Equilibrium Level of Aggregate Income both inAlgebra and Geometry.(PEQ4 Page168; 2012Mid1 M23-M27 Page 195-196; M34 Page198 ; E3 Page 201)



Consumption and Saving Function

Let b = MPC(Definition e.g. M28,S = Y − C = Y − (a + bY ) =−a + (1− b)Y e.g.M30;b = ∆C

∆Y and 1− b = ∆S∆Y e.g. M29

E : Zero Saving Y2 = C2 ⇒ S2 = 0

Saving Y3 > C3 ⇒ S1 > 0 by the amount |CD|or |C ′D′| e.g. M32

Dissaving Y1 < C1 ⇒ S2 < 0 by the amount|AB| or |A′B′|





∆Y and 1− b = ∆S∆Y e.g. M29








∆Y and 1− b = ∆S∆Y e.g. M29








∆Y and 1− b = ∆S∆Y e.g. M29






Aggregate Expenditure Line

AE = C + I = a + bY + I = (a + I) + bY , soY-intercept is a + I and slope is b(MPC)

Equilibrium:Y3 = AE = C + I ⇒ S3 = I(|FG| = |F ′G′|)(no unplanned inventories or no change ininventories)

DisequilibriumY5 < C5 + I ⇒ S5(|MN| = |M ′N ′|) < I(|FG|)(unplanned inventories< 0 or inventories arefalling)

DisequilibriumY4 > C4 + I ⇒ S4(|PQ| = |P ′Q′|) > I(|FG|)(unplanned inventories> 0 or inventories arerising) e.g M34
























Comparative Statics

Comparative Statics : Everything else staying the same, we analyzehow a change in one parameter would affect curves and thereforeoutcome equilibrium.

Autonomous(a) ↑⇒ C(S) Line shifts up(down) parellel⇒AE Line shifts up parellel⇒ Equil. Y ↑; Equil. C ↑; Equil. S↔ and viceversa.Graphics; (The paradox of thrifty), e.g. PEQ4 Part 2 (c)

MPC(b) ↑⇒ C(S) Line rotates up(down)⇒ AE Line rotates up⇒Equilibrium Y ↑; Equil. C ↑; Equil. S↔ and vice versa.Graphics e.g. M33

Planned Investment(I) ↑⇒ AE Line shifts up parellel⇒ Equilibrium Y ↑; Equil. C ↑; Equil. S ↑ and vice versa.

Graphics; (Investment Multiplier Effect), e.g. PEQ4 Part 1 (c)

Back



Comparative Statics: Change in Autonomous Consumption

The change to C(S) lines with anincrease in a

The change to AE lines with anincrease in a

Back



Comparative Statics:Change in MPC or MPS

The change to C(S) lines with anincrease in MPC

The change to AE lines with anincrease in MPC

Back



Comparative Statics:Change in Planned Investment

The change to AE lines with anincrease in I

Multiplier Effect given an increasein I

Back



Consumption and Saving Function:Example

2012Mid1 M28 Page 19628. The fraction of a change in income that is consumed or spent iscalled

A the marginal propensity of income

B the marginal propensity to save

C the marginal propensity to consume

D average consumption

Back




2012Mid1 M28 Page 19628. The fraction of a change in income that is consumed or spent iscalled

A the marginal propensity of income

B the marginal propensity to save

C the marginal propensity to consume

D average consumption

Back




2012Mid1 M29 Page 19629. Suppose saving is $2000 when income is $10,000 and MPCequals 0.8. When income increases to $15,000, saving is

A $4,000

B $3,000

C $2,400

D $5,000

Back




2012Mid1 M29 Page 19629. Suppose saving is $2000 when income is $10,000 and MPCequals 0.8. When income increases to $15,000, saving is

A $4,000

B $3,000

C $2,400

D $5,000

Back




2012Mid1 M29 Page 196Solution: Let S1 = $2000, Y1 = 10, 000, Y2 = 15, 000,so we have

1−MPC = ∆S∆Y

(1)

1− 0.8 = S2 − S1

Y2 − Y1(2)

0.2 = S2 − 2, 00015, 000− 10, 000

(3)

(4)

Rearranging terms, S2 = $3, 000Back




2012Mid1 M30 Page 19630. Assume the economy has only households and firms, and thesaving function is S=-20+.3Y, then consumption at an income level of114 would be

A 100

B 90

C 110

D 50

Back




2012Mid1 M30 Page 19630. Assume the economy has only households and firms, and thesaving function is S=-20+.3Y, then consumption at an income level of114 would be

A 100

B 90

C 110

D 50

Back




2012Mid1 M30 Page 196Solution: Method 1: By using the relationship between consumptionand saving functionC = 20 + 0.7Y so if Y = 114, thenC = 20 + 0.7× 114 = 99.8 ≈ 100Back




2012Mid1 M30 Page 196Solution: Method 1: By using the relationship between consumptionand saving functionC = 20 + 0.7Y so if Y = 114, thenC = 20 + 0.7× 114 = 99.8 ≈ 100Method 2: Plugging Y = 114 into S,S = −20 + 0.3Y = −20 + 0.3× 114 = 14.2So C = Y − S = 114− 14.2 = 99.8 ≈ 100Back




2012Mid1 M31 Page 19731. Assume that a consumption function is C = 200 + .2Y. Themarginal propensity to save is

A 0.8.

B 0.75.

C 0.25.

D 0.2.

Back




2012Mid1 M31 Page 19731. Assume that a consumption function is C = 200 + .2Y. Themarginal propensity to save is

A 0.8.

B 0.75.

C 0.25.

D 0.2.

Back




2012Mid1 M32 Page 19732. Refer to the informationprovided in Figure 8.2 below toanswer the question that follows.At point C, Jerry’s

A consumption equals his income.

B consumption is greater than hisincome.

C saving is zero.

D saving is positive.Back




2012Mid1 M32 Page 19732. Refer to the informationprovided in Figure 8.2 below toanswer the question that follows.At point C, Jerry’s

A consumption equals his income.

B consumption is greater than hisincome.

C saving is zero.

D saving is positive.Back




2012Mid1 M33 Page 19733. Refer to the information provided inFigure 8.1 below to answer the question thatfollows.Refer to Figure 8.1. An increase in MPC

A makes the consumption function flatter.

B makes the saving function flatter.

C shifts the consumption function upward.

D shifts the saving function downward.

E makes the saving function steeper.Back




2012Mid1 M33 Page 19733. Refer to the information provided inFigure 8.1 below to answer the question thatfollows.Refer to Figure 8.1. An increase in MPC

A makes the consumption function flatter.

B makes the saving function flatter.

C shifts the consumption function upward.

D shifts the saving function downward.

E makes the saving function steeper.Back




2012Mid1 M34 Page 19834. Suppose actual investment is greater than planned investment.Given this information, we know with certainty that

A the economy is in equilibrium.

B firms’ inventories are not changing.

C output will tend to fall.

D saving is negative (S < 0).

Back




2012Mid1 M34 Page 19834. Suppose actual investment is greater than planned investment.Given this information, we know with certainty that

A the economy is in equilibrium.

B firms’ inventories are not changing.

C output will tend to fall.

D saving is negative (S < 0).

Back



Table of Contents

1 Aggregate Expenditure Model

2 Practice Essay Question 4



PEQ 4 Part 1 Page 167

Part 1 [Macroeconomic Equilibrium] Assume consumption isrepresented by the following: C = 400 + .75Y . Also assume thatplanned investment (I) equals 100.




a. Given the information, calculate the equilibrium level of income.




a. Given the information, calculate the equilibrium level of income.We are given C = 400 + 0.75Y; I = 100.Using Equilibrium Condition:Y = C + I NationalIncome=Aggregate Expenditure, we get

Y = 400 + 0.75Y + 100∗

0.25Y = 500Y = 2000

Back

∗Move 0.75Y to the leftZheng Zhang Chapter 8: Aggregate Expenditure and Equilibrium Output



Further thought: now let’s try to derive a general formula for the levelof equilibrium income using C = a + MPC × Y and I:

Y = a + MPC × Y + I(1−MPC)× Y = a + I

Y = a + I1−MPC

ora + IMPS

Back




Remark IEquilibrium level of income can be split into two parts: one is a

MPSwhich can be interpreted as the aggregate output supported byautonomous consumption and the other is I

MPS which, in a similarfashion, is interpreted as the output supported by plannedinvestment.The marginal consuming behavior by households as afraction of their incomes then gives rise to multiplier effect. Back




Remark IIThis result is also useful in computation,for example,in yourHomework Question 9, if I know a = 0 and I = 75 andMPS = 0.25, I can calculate equilibrium level Y = 75/0.25 = 300.So I know the trull level is on the left side of equilibrium point, thenunplanned inventories have to fall and aggregate output will increaseto equilibrium level. And also, in your quiz, you are given a similarquestion without specifying a, but actually it’s not necessary, becauseyou can see Y ≥ I

MPS so you can judge which is greater, equilibriumlevel or real level. Back



PEQ 4 Page 167

b. Given the information, calculate the level of consumption andsaving that occurs at the equilibrium level of income.



PEQ 4 Page 167

b. Given the information, calculate the level of consumption andsaving that occurs at the equilibrium level of income.Method 1: Without doing calculation, using equilibrium conditiongives S = I = 100† , then C = Y − S = 2000− 100 = 1900Method 2:C = 400 + 0.75Y ;⇒ C = 400 + 0.75× 2000 = 1900‡

S = Y − C = 2000− 1900 = 100Back

† this only holds for basic model without government and closed economy‡plug Y back in consumption function



PEQ 4 Page 167

c. Suppose planned investment increases by 100. Calculate the newequilibrium level of income. Given your answer, what is the size ofthe multiplier for this economy?



PEQ 4 Page 167

c. Suppose planned investment increases by 100. Calculate the newequilibrium level of income. Given your answer, what is the size ofthe multiplier for this economy?We are given C’ = 400 + 0.75Y’; I’ = 100+100=200.

Y ′ = 400 + 0.75Y ′ + 2000.25Y ′ = 600

Y ′ = 2400

Multiplier = 1 / (1-MPC)=1/(1-0.75) = 4Back



PEQ 4 Part 1Page 167

d. Will the level of saving and consumption change as the economyadjusts to this change in planned investment?




d. Will the level of saving and consumption change as the economyadjusts to this change in planned investment?Method 1: S′ = I ′ = 200 andC ′ = Y ′ − I ′ = 2400− 200 = 2200(compare the result with Q(b))Method 2:C′ = 400 + 0.75Y ′ ⇒ C′ = 400 + 0.75× 2400 = 2200To compute S’, S′ = Y ′ − C′ = 2400− 2200 = 200Yes, both C and S will rise as Y rises.Back




Remark

(a) Have you noticed that ∆Y = ∆I ×Multiplier where∆Y = Y ′ − Y = 2, 400− 2, 000 = 400 and∆I = I ′ − I = 200− 100 = 100 So this gives a shortcut tocalculate the new equilibrium level of income given a change inInvestment:Let’s do Q(c) again Using ∆I = 100,∆Y = ∆I ×Multiplier = 100× 4 = 400. Therefore,we can figure out Y ′ = Y + ∆Y = 2000 + 400 = 2400. In thefuture, you can take this shortcut.

(b) Can you draw this change in I in the Keynesian Cross?What’s therelationship between two curves?

Back




Part 2. [Macroeconomic Equilibrium] Assume consumption isrepresented by the following: C = 200 + .75Y . Also assume thatplanned investment (I) equals 300.




a. Given the information, calculate the equilibrium level of income.




a. Given the information, calculate the equilibrium level of income.C = 200 + 0.75Y; I = 300Using equilibrium condition Y = C + I, we get

Y = 200 + 0.75Y + 3000.25Y = 500

Y = 2000

Back




b. Given the information, calculate the level of consumption andsaving that occurs at the equilibrium level of income.




b. Given the information, calculate the level of consumption andsaving that occurs at the equilibrium level of income.Method1: Without doing calculation, using the equilibrium conditionthat S = I = 300 and then C = Y − S = 2000− 300 = 1700Method2: C = 200 + 0.75Y ; C = 200 + 0.75× 1700S = Y − C = 2000− 1700 = 300Back




c.Now suppose that individuals decide to increase their saving so thatautonomous consumption falls by 100. The consumption function isnow C = 100 + .75Y . Calculate the new equilibrium level ofincome, the new level of consumption, and the new level of saving.




c.Now suppose that individuals decide to increase their saving so thatautonomous consumption falls by 100. The consumption function isnow C = 100 + .75Y . Calculate the new equilibrium level ofincome, the new level of consumption, and the new level of saving.We are given C′ = 100 + 0.75Y ; I = 300Then using equilibrium condition Y ′ = C′ + I gives

Y ′ = 100 + 0.75Y ′ + 3000.25Y ′ = 400

Y ′ = 1600

Plugging Y back in consumption function, we get C’ = 1300 ; S’=Y’-C’= 300Back




d.Based on your analysis in Part (c), did the level of saving change asa result of this increased desire to save? Explain.




d.Based on your analysis in Part (c), did the level of saving change asa result of this increased desire to save? Explain.Saving did not change as a result of this increased desire to save. Thisis simply a numerical application of the paradox of thrift .With I unchanged, the level of saving will return to its original level(while consumption falls).Back




(a) Comparing the result of Part I Q(a) and Part 2 Q(a), we foundthe levels of equilibria for two model are the same, is it acoincidence? Can you draw graph to show this? In addition, ineconomics, we call the study of contrasting two models with thesame set-up and different parameters Comparative Statics .

(b) Does a change in autonomous consumption affect an economythe same way a change in investment does? Look at Q(c) againand suppose, instead, the investment falls by 100 and other thingsstay the same, How would Y, C and I change respectively?

Back


Documents

Chapter 8: Aggregate Expenditure and Equilibrium …publish.illinois.edu/zzhangecon/files/2014/09/Chapter8_slides.pdfAggregate Expenditure Model Practice Essay Question 4 Chapter 8: